Advertisement

An Asymptotic Theory for Estimating Beta-Pricing Models Using Cross-Sectional Regression

Authors

  • Ravi Jagannathan,

    1. Kellogg Graduate School of Management, Northwestern University, Carlson School of Management, University of Minnesota
    Search for more papers by this author
  • Zhenyu Wang

    1. Graduate School of Business, Columbia University
    Search for more papers by this author
    • Jagannathan is from the Kellogg Graduate School of Management, Northwestern University, and the Carlson School of Management, University of Minnesota. Wang is from the Graduate School of Business, Columbia University. We appreciate comments from David Backus, Sid Browne, Edwin Elton, Pierre Hillion, Bob Hodrick, and Raymond Kan, as well as seminar participants at the 1998 meeting of the American Finance Association, Columbia University, Northwestern University, University of Minnesota, Federal Reserve Bank of New York, and Stockholm School of Economics. Errors are our own. We thank Laarni Bulan for research assistance. Ravi Jagannathan acknowledges partial financial support from the National Science Foundation, grant SBR-9409824.

ABSTRACT

Without the assumption of conditional homoskedasticity, a general asymptotic distribution theory for the two-stage cross-sectional regression method shows that the standard errors produced by the Fama–MacBeth procedure do not necessarily overstate the precision of the risk premium estimates. When factors are misspecified, estimators for risk premiums can be biased, and the t-value of a premium may converge to infinity in probability even when the true premium is zero. However, when a beta-pricing model is misspecified, the t-values for firm characteristics generally converge to infinity in probability, which supports the use of firm characteristics in cross-sectional regressions for detecting model misspecification.

Ancillary